Mathematics 0580/22 October/November 2024: question paper and mark scheme

Question

These are the first eight terms of a sequence. c -3 -9 -15 -21 -27 -33 k Find the value of c and the value of k. c = …… k = …… [2]

Question

The diagram shows an isosceles triangle. x° NOT TO SCALE 43° Find the value of x. x = …… [2]

Question

1 0.25 3.142 3 -3 24 - 0.4 1.2 - 4 Complete each statement with a number from the list. …… is a natural number. …… is an irrational number. …… is the reciprocal of 4. [3]

Question

The scatter diagram shows the number of rooms and the number of people in each of eight buildings. 70 60 50 40 Number of rooms 30 20 10 0 0 10 20 30 40 50 60 70 80 Number of people (a) One of the buildings has 67 rooms. Write down the number of people in this building. …… [1] (b) In another building there are 42 people and 33 rooms. On the scatter diagram, plot this point. [1] (c) (i) On the scatter diagram, draw a line of best fit. [1] (ii) There are 45 people in a different building. Find an estimate for the number of rooms in this building. …… [1] (d) What type of correlation is shown in the scatter diagram? …… [1]

Question

Convert 7.51 m 2 into cm 2 . …… cm 2 [1]

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The diagram shows a trapezium. NOT TO 9.5 cm x cm SCALE 6 cm The area of the trapezium is 42 cm 2 . Calculate the value of x. x = …… [2] 2 6

Question

Without using a calculator, work out ' . 7 11 You must show all your working and give your answer as a fraction in its simplest form. …… [2]

Question

The diagram shows a parallelogram. (132 – 2x)° NOT TO SCALE (15 + 5x)° Work out the size of the smallest interior angle of the parallelogram. …… [4]

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A B NOT TO SCALE D C Points A, B, C and D lie on a circle. ABCD is a square with area 72 cm 2 . Calculate the area of the circle. Give your answer as a multiple of r . …… cm 2 [3] 3

Question

Calculate 1 + 10.9 # 0.4 2 . …… [1]

Question

Factorise fully. (a) 24x 2 - 9xy …… [2] (b) 63x 2 - 28y 2 …… [3] 12 y is directly proportional to the square root of x + 1. y = 10.5 when x = 8 . Find y when x = 1.56 . y = …… [3]

Question

In the question paper above.

Question

y 5 4 3 2 1 –5 –4 –3 –2 –1 0 1 2 3 4 5 x –1 –2 –3 –4 –5 The region R satisfies these inequalities. -3 1 y G 2 y G x-1 By drawing suitable straight lines and shading unwanted regions, find and label the region R. [4]

Question

20 NOT TO SCALE Speed (m/s) 0 0 10 17 Time (seconds) The diagram shows the speed–time graph for 17 seconds of a car journey. (a) Find the acceleration of the car during the first 10 seconds. …… m/s 2 [1] (b) Calculate the total distance travelled by the car during the 17 seconds. …… m [3]

Question

At the start of an experiment there are 40 000 bacteria. The number of bacteria increases at a rate of 15% per hour. Calculate the number of bacteria after 3 hours. …… [2] 16 75 people are asked if they have a car, C, and if they have a job, J. The Venn diagram shows the results. % C J 9 51 13 2 A person is chosen at random from those who have a car. Find the probability that this person also has a job. …… [1]

Question

In the question paper above.

Question

A B 64° D x° O NOT TO SCALE C A, B and C are points on the circumference of a circle with centre O. DA and DC are tangents to the circle. Angle ABC = 64°. Work out the value of x. x = …… [2]

Question

(a) % = {8 # 10 -1 , 0.8o , 8%, 0.08} A = { a: 0.08 1 a G 0.8 } B = { b: b H 0.8 } % A B Complete the Venn diagram. [3] (b) Shade the region (A , C ) + Bl in the Venn diagram. % A B C [1]

Question

4.3 cm NOT TO SCALE 11.9 cm A solid is made from a cylinder and a hemisphere, both of radius 4.3 cm. The cylinder has length 11.9 cm. (a) Calculate the volume of the solid. 4 [The volume, V, of a sphere with radius r is V = rr 3 .] 3 …… cm 3 [3] (b) Calculate the total surface area of the solid. [The surface area, A, of a sphere with radius r is A = 4rr 2 .] …… cm 2 [4]

Question

Find an expression for the nth term of this sequence. 1 , 1, 7, 49, 343, 2401, … 7 …… [2]

Question

Expand and simplify. (x + 3) (x + 5) (2x + 1) …… [3]

Question

A is the point (17, 9) and B is the point (23, 39). Find the equation of the perpendicular bisector of line AB. Give your answer in the form y = mx + c . y = …… [5] Question 23 is printed on the next page.

Question

NOT TO SCALE x cm 3.5 cm Small box Large box The small box is mathematically similar to the large box. The volume of the large box is 72.8% greater than the volume of the small box. The small box has length 3.5 cm and the large box has length x cm. Calculate the value of x. x = …… [3]